Let f(x) = 2x² + 14x – 16 and g(x) = x+8. Perform the function operation and then find the domain of the result.(x) = (simplify your answer.)

Answer:

gr,wrgñegetjj

Step-by-step explanation:

jyyjytjjttj

Answer:

Step-by-step explanation

Rs 3200 for 20 students for 30 days

so,

3200÷20×30 = 16/3 rs per day

for Rs 2400 for 30 students. let the no. of students be X

so,

16/3 = 2400/30×X

So, X = 15 days

ans. food will last for 15 days

The following that represent the sales price and the regular prices are:

regular price: $55.43, sales price: $45.45

regular price: $29.99,  sales price: $24.59

regular price: $652.30, sales price: $534.89

Percentage is the fraction of a number out of hundred. The sign that is used to represent percentages is %.

When a discount is given on the price of an item, the price of the item would reduce by the given price or by the percent reduction.

Sales price = regular price x (1 - discount)

Sales price = regular price x (1 - 0.18)

Sales price = regular price x 0.82

Sales price when the initial price is $55.43: $55.43 x 0.82 = $45.45

Sales price when the initial price is $29.99: $29.99 x 0.82 = $24.59

Sales price when the initial price is $215.33: $215.33 x 0.82 = $176.57

Sales price when the initial price is $849.50: $849.50 x 0.82 = $696.59

Sales price when the initial price is $652.30: $652.30 x 0.82 = $534.89

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We are given the formula y=x. The easiest way to graph the equation of a line is simply by giving some values of x and the joining all the points. Consider the following

X Y

-2 -2

-1 -1

0 0

1 1

2 2

3 3

If we graph this points and the join them with a line, we get

Answer:

If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)

If leg b is unknown, then: b = √(c² - a²)

For hypotenuse c missing, the formula is: c = √(a² + b²)

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf P= 9 \ in. }\)

Step-by-step explanation:

Given is a right-angled triangle.

So, we can use Pythagorean Theorem to find the missing length.

It is:

\((Hypotenuse)^2=(Base)^2+(Perpendicular)^2\)

Here,

Hypotenuse = 41 in.

Base = 40 in.

Perpendicular = P

\((41)^2=(40)^2+P^2\\\\1681 = 1600 + P^2\\\\Subtract \ 1600 \ from \ both \ sides\\\\1681-1600=P^2\\\\81 = P^2\\\\Take \ square \ root \ on \ both \ sides\\\\\sqrt{81} = \sqrt{P^2} \\\\P= 9 \ in. \\\\\rule[225]{225}{2}\)

Answer:

1, 16, 100

Step-by-step explanation:

Answer:

other persons right i took the test and got it right so 1, 16, and, 100

Step-by-step explanation:

A binomial with degree 2 is a binomial squared, square binomial (or binomials squared) are those in which the sum or subtraction of two terms must be raised to the power of two.

Among the 4 options, the one that meets these criteria would be the following one.

Evidently here we have a subtraction between two terms raised to the power of 2.

In conclusion, the answer is:

Answer:

32.0 cm

Step-by-step explanation:

volume of a hemisphere = (2/3)πr3

r = cube root (Volume * 3/2 * 1/π )

r = cube root ( 8514 * 3/2 * 1/π)

r = 15.96

in the nearest tenth r = 16.0 cm

D= 2r

D= 2(16)

D= 32cm

Answer: 31.9 cm

Step-by-step explanation:

Got it from deltamath so it's right

The domain is the set of all the x-values/inputs used by the function.  

The range is the set of all y-values/outputs used by the function.

For #1:

The domain is { 1, 0, -1, 4 } because those are the x-values.

The range is { 3, 5, 7, -6 } because those are the x-values.

I'll let you try #2.  if you write back with your answer, I'll reply to let you know if you did it correctly.

Answer:

2-×+3-×-4=0

Step-by-step explanation:

×=1\2

0.5,2`1

Where's the question??

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

Answer:

The time it will take is approximately 104,128 seconds

Step-by-step explanation:

The given parameters are;

The diameter of the tank, D = 24 ft.

Therefore, the tank radius, R = D/2 = 24 ft./2 = 12 ft.

The height of the tower on which the tank sits, h = 60 ft.

The hose through which the tank is filled is attached at the bottom of the tank

The radius of a slice of sphere, r = √(R² - y²) = √(12² - y²)

The power of the pump which is used to deliver the water = 1.5 horsepower

The volume of a slice of water in the tank, V = π·r²·Δx = π·(√(12² - y²))²·Δx ft³ = (144 - y²)·π·Δx ft³

The force of the slice, F = V·g·ρ = (144 - x²)·π·Δx ft³ × 62.5 lb/ft³

Let '\(y_i\)' represent the height to which each slice is pumped in  the tank, we have;

y = R - (√(R² - x²)) = 12 - (√(144 - x²)

\(\lim\limits_{n \to \infty}\ \sum\limits_{i=0}^n (144 - x^2) \cdot \pi \times 62.5 \cdot y_i\ \Delta x \ lb\)

The work done is therefore;

\(W = 62.5\times\pi \times \int\limits^{12}_{-12} {(144 - x^2) \cdot(12-(\sqrt{144-x^2} ) \ } \, dx = 632044.366475 \ ft. \cdot lb\)

The work done in filling the tank, W = 632,044.366475 ft·lb

The work done in lifting the water to the base of the tank, W₂ = V·ρ·g×h

\(\therefore W_2 = 60 \times 62.5\times\pi \times \int\limits^{12}_{-12} {(144 - x^2) \ } \, dx = 632044.366475 \ ft. \cdot lb = 85273382.0257\)

Therefore, W₂ = 85,273,382.0257 ft.lb

The total work done by the pump,

W = 85,273,382.0257 ft.lb + 632,044.366475 ft·lb = 85,905,426.3922 ft.lb

The time it will take the pump to fill the tank, 't', is given as follows;

1

Power, P = Work, W/(Time, t)

∴ t = W/P

P = 1.5 HP = 550 × 1.5 ft·lb/s = 825 ft·lb/s

t = 85,905,426.3922 ft.lb/(825 ft·lb/s) = 104,127.789566 s

The time it will take, t ≈ 104,128 seconds

Answer:

the answer is nine ,but I don't know it to the nearest hundredth

Las cantidades de bolitas para cada una de las tres personas son las siguientes:

Amanda: 19 bolitas

Rodrigo: 15 bolitas

Patricio: 69 bolitas

En este problema tenemos a tres personas (Amanda, Rodrigo y Patricio) que se reparten 103 bolitas, en términos algebraicos, cada persona es representada por las siguientes ecuaciones:

Amanda

x = y + 4

Rodrigo

y

Patricio

z = 2 · (x + y) + 1

Total

x + y + z = 103

A continuación, determinamos la cantidad de bolitas asociada con Rodrigo:

x + y + 2 · (x + y) + 1 = 103

3 · x + 3 · y = 102

x + y = 34

y + 4 + y = 34

2 · y = 30

y = 15

Luego, determinamos las cantidades de bolitas de Amanda y Patricio:

x = 15 + 4

x = 19

z = 2 · (19 + 15) + 1

z = 2 · 34 + 1

z = 68 + 1

z = 69

El enunciado se encuentra escrito en español y el lenguaje de la respuesta es el mismo del enunciado.

The statement is written in Spanish and the language used in the answer is the same of the statement.

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Answer:

100k each without tax + interest

Step-by-step explanation:

Answer:

For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.

Step by Step:

Keep this in mind >>

Consider the unit circle > The sine and cosine ratios are the only ratios that have 1 (the radius or hypotenuse) as the denominator. The numerators (sides) vary between 0 and 1, thus determining that the sine and cosine do the same.

All of the other ratios (tangent, cotangent, secant, cosecant) have a side as the denominator, varying between 0 and 1. As any denominator approaches 0, the value of the ratio approaches infinity.

The cost per pound of rib steak is $2.40 and the cost per pound of hamburger meat is $1.25.

To find the cost per pound of each type of meat, we can set up a system of equations based on the given information.

Let's denote the cost per pound of rib steak as 'x' and the cost per pound of hamburger meat as 'y'.

From the first statement, we know that:

2x + 6y = 12.30 ---(Equation 1)

From the second statement, we know that:

3x + 2y = 9.70 ---(Equation 2)

Now we can solve this system of equations to find the values of 'x' and 'y'.

Multiplying Equation 1 by 3 and Equation 2 by 2 to eliminate the 'x' term, we get:

6x + 18y = 36.90 ---(Equation 3)

6x + 4y = 19.40 ---(Equation 4)

Subtracting Equation 4 from Equation 3, we get:

14y = 17.50

Dividing both sides by 14, we find:

y = 1.25

Substituting the value of 'y' back into Equation 1, we can solve for 'x':

2x + 6(1.25) = 12.30

2x + 7.50 = 12.30

2x = 4.80

x = 2.40

Therefore, the cost per pound of rib steak is $2.40 and the cost per pound of hamburger meat is $1.25.

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The value of x is 65°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:
Angle PQR is a right angle.

The measure of angle SQR is 25 degrees.

The measure of PQS is x degrees.

The angle addition postulates:

∠PQR = ∠SQR  + ∠PQS

90° = 25° + x

x = 90° - 25°

x = 65°

Hence, ∠PQS = 65°.

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A perimeter longer than 50 for any point, C satisfies the area requirement.

Consequently, we have a base-10 triangle whose area is 100. Since the area is equal to half the product of base and height, the object's height is then 20.

The next two sides. If one of the sides is exactly 20 inches tall (when it coincides with the height, forming a right triangle), the other side must be strictly greater than 20 inches tall (being the hypotenuse), in which case the perimeter must be greater than 50.

Alternately, both sides could be longer than 20 because neither side is a height. Once more, the perimeter exceeds 50.

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The full question

In a given plane, points A and B are 10 units apart. How many points C are there in the plane such that the perimeter of triangle ABC is 50 units and the area of triangle ABC is 100 square units?

Compute the derivative dy/dx using the power, product, and chain rules. Given

x³ + y³ = 11xy

differentiate both sides with respect to x to get

3x² + 3y² dy/dx = 11y + 11x dy/dx

Solve for dy/dx :

(3y² - 11x) dy/dx = 11y - 3x²

dy/dx = (11y - 3x²)/(3y² - 11x)

The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when

11y - 3x² = 0

or

y = 3/11 x²

(provided that 3y² - 11x ≠ 0)

Substitute y into into the original equation:

x³ + (3/11 x²)³ = 11x (3/11 x²)

x³ + (3/11)³ x⁶ = 3x³

(3/11)³ x⁶ - 2x³ = 0

x³ ((3/11)³ x³ - 2) = 0

One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with

(3/11)³ x³ - 2 = 0

(3/11 x)³ - 2 = 0

(3/11 x)³ = 2

3/11 x = ³√2

x = (11•³√2)/3

Solving for y gives

y = 3/11 x²

y = 3/11 ((11•³√2)/3)²

y = (11•³√4)/3

So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).

Total number of rabbits produced in 9 years will be 45.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a rabbit can produce 5 new rabbits per year

Total number of rabbits produced in 9 years will be -

n = 5y = 5 x 9 = 45 new rabbits

Therefore, total number of rabbits produced in 9 years will be 45.

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The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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Answer:

Step-by-step explanation:

we know that

In a  triangle

the ratio between the lengths of the two legs is equal to the tangent

so

therefore

the answer is

Option B

-------> could be the ratio

because is the value of the

Option C

------> could be the ratio

because is the value of the

Option E

-------> could be the ratio

because is the value of the

The options B, C and E giving the ratios are correct.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.

Given that, a 30-60-90 right triangle, we need to find the ratio between the lengths of the two legs of the triangle,

Since, we know that,

In a right triangle, the ratio between the lengths of the two legs is equal to the tangent.

so,

Tan 30° = 1/√3

Also,

√3 / 3 = 1/√3

3/3√3 = 1/√3

Hence, the options B, C and E giving the ratios are correct.

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Answer:

2000

Step-by-step explanation:

203750-199532 = 4218

This the the greatest difference

Based on the calculations, the year in which the actual population of Center City is most different from the value predicted by this model is: C. 2000.

A linear model can be defined as an equation that indicates the relationship existing between two (2) quantities with a constant rate of change.

Next, we would find the differences:

1985 to 1990 = 197,800 - 194,957 = 2,843.

1992 to 2000 = 203,750 - 199,532 = 4,218.

2005 to 2012 = 210,600 - 206,561 = 4,039.

In conclusion, the year in which the actual population of Center City is most different from the value predicted by this model is 2000.

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Answer:

44

Step-by-step explanation:

vertical angles

Answer:

-12

Step-by-step explanation:

3/5 * (1 + sqrt(16))^2 - (5 - 2)^3 =

= 3/5 * (1 + 4)^2 - (3)^3

= 3/5 * (5)^2 - 27

= 3/5 * 25 - 27

= 15 - 27

= -12

The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41

The equation of the line in standard form can be represented as follows:

Ax + By = C

where

Therefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;

Parallel lines have the same slope.

Hence,

3y = 4x + 8

y = 4  / 3 x + 8 / 3

The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.

y = 4 / 3 x + b

-3 = 4 / 3 (8) + b

b = -3 - 32 / 3

b =  -9 - 32/ 3

b = -41 / 3

Hence,

y = 4 / 3 x - 41 / 3

multiply through by 3

3y = 4x - 41

Therefore, the standard form is 4x - 3y = 41

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